Answer:
.75 is your answer
Step-by-step explanation:
1. False (F): Example: 2-3=-1∉N
2. True (T)
3. True (T)
4. False (F): Example: 3/4=0.75 which is not an integer
5. False(F) : Ratio can be negative if one but not the other integer is negative. Example: 5 : (-1)= -5
6. True (T)
7. True (T)
<h3>
Answer: B) 43, 133, 89</h3>
===========================================================
Explanation:
For this answer choice, we have p = 43, q = 133, and r = 89. Note how p+r = 43+89 = 132, which is <u>not</u> larger than the third remaining side q = 133. Therefore, p+r > q is false and a triangle cannot be formed.
A triangle is only possible if and only if adding any two sides leads to a sum larger than the third side (triangle inequality theorem).
Put another way, we must have these three conditions hold true for a triangle to form:
If any of those three are false, then we cannot make a triangle with side lengths p,q,r
-----------------
Let's go over choice C for an example in which we can form a triangle
p = 5, q = 6, r = 7
We can see that,
- p+q = 5+6 = 11 which is greater than r = 7. So p+q > r is true.
- p+r = 5+7 = 12 which is greater than q = 6. So p+r > q is true.
- q+r = 6+7 = 13 which is greater than p = 5. So q+r > p is true.
All three conditions are true, and therefore we have a triangle that is possible with side lengths p = 5, q = 6, r = 7. I recommend cutting out slips of paper with these lengths to try it out yourself, so you have a real world example to play with. Choices A and D are a similar story to choice C, so we can rule out all three of these choices.
The answer is 32 degrees. APEX
Answer:
Domain- Interval Notation:
(
−
∞
,
∞
)
Set-Builder Notation:
{
x
|
x
∈
R
}
Range- Interval Notation:
(
−
9
,
∞
)
Set-Builder Notation:
{
y
|
y
>
−
9
}
Step-by-step explanation:
Horizontal asymptote- y=-9
